Confidence intervals?

Question

the z value corresponding to a 97 percent confidence interval is?

a) 1.88

b) 2.17

c)1.96

d) 3 percent

Please explain .thanks

Answer 1

ANSWER b) 2.17

Why??

"z value" related to a Normal Distribution.  Normal Distribution has "z value" on the x-axis and has "Probability" on the y-axis.  The Textbook has a Table showing "z value" and a probability for each "z value".  "z value" is negative and positive.  When "z value" = 0, that is the middle "mean" of the Normal Distribution.  50% of the Normal Distribution are for all "z value" negative and 50% are "z value" positive.

Question is 97 percent which means 48.5 percent on one side of Normal Distribution and 48.5 percent on the other side.  This corresponds to z = 2.17.

Table for Normal Distribution is "Cumulative". Table shows "z value" = -2.17 for probability 0.0150 and "z value" = 2.17 for probability 0.9850.

Subtract 0.9850 - 0.0150 = 0.9700 (97%)